The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number for special cases, but no general description has been proposed. Here, we present a covariant WKB analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis reported here is analogous to the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.

中文翻译：

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引力自旋霍尔效应的光

电磁波在真空中的传播通常是在几何光学近似中描述的，它可以预测波射线遵循零短程线。但是，该模型仅在无限高的频率范围内有效。在较大但有限的频率下，衍射仍然可以忽略不计，但是射线动力学受到波偏振演化的影响。因此，光线可能会偏离零距离大地测量学，这被称为光的重力自旋霍尔效应。在文献中，已经针对一些特殊情况临时计算了这种影响，但是没有提出一般描述。在这里，我们从光在任意弯曲时空中传播的第一原理介绍了协变WKB分析。我们获得描述光的重力自旋霍尔效应的偏振相关射线方程。我们还提供了Schwarzschild时空中与偏振有关的射线动力学的数值示例，并简要讨论了影响的大小。此处报道的分析类似于光在非均匀介质中的自旋霍尔效应，该效应已通过实验验证。